Chu Chi tunnels or Cu Chi tunnels?

Chu Chi tunnels or Cu Chi tunnels?

Chu Chi tunnels or Cu Chi tunnels - Which one is right name? It may sounds similar by visitors but Vietnamese says “ Cu Chi”.
Why it name Cu Chi?
The name of the District Cu Chi which located 40 km in the North – west of HCM City.
In Nguyen Dynasty Cu Chi belong to Binh Duong distric, Tan Binh, Phien An. In 1836, Cu Chi became part of Binh Duong District, Gia Dinh Province. In 1956 Cu Chi became a new district of Binh Duong. In 1963, South Vietnam setup Hai Nghia province and half of Cu Chi remain the same name and belong to Hai Nghia Province. The other half belong to Phu Hoa, Binh Duong province.